Combine 2 gallons water and salt in a large container, stirring with a whisk until salt dissolves. Add cucumbers; let stand at room temperature for 12 hours.
Place 2 teaspoons mustard seeds, 2 dill sprigs, and 1 garlic clove half in each of 12 (1-pint) hot sterilized jars. Drain cucumbers; divide among jars.
Combine vinegar, 4 cups water, sugar, and pickling spice in a large saucepan. Bring to a boil; cook 10 minutes. Divide hot vinegar mixture evenly among jars, filling to 1/2 inch from top. Remove air bubbles; wipe jar rims. Cover with metal lids; screw on bands.
Process in boiling-water bath for 20 minutes. Remove jars from water bath; cool completely, and check for proper seal (see Note below). For best flavor, allow 2 weeks before eating. Store pickles in a cool, dark place for up to 1 year.
Note: Remove jars from canner, placing on a towel. Let jars stand at room temperature 12 to 24 hours. Press center of each lid; lids should not flex or "pop." Remove bands; gently try to lift lid with gentle pressure. If lid stays on, you have a good seal.